Category: Part 2: Thermodynamics

Problem Statement Solve the fluid mechanics problem: Solve the fluid mechanics problem: Find the osmotic pressure of a $0.1\ \text{mol/L}$ solution of glucose in water at $T=300\ \text{K}$. Van’t Hoff’s law (dilute solutions behave like ideal gases): $$\Pi = \nu RT/V = cRT$$ where $c = 0.1\ \text{mol/L} = 100\ \text{mol/m}^3$. $$\Pi = 100\times8.314\t Given…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A metal sphere of mass $m=0.5\ \text{kg}$, specific heat $c=400\ \text{J/kg·K}$, surface area $A=0.04\ \text{m}^2$ is in air with heat transfer coefficient $h=20\ \text{W/m}^2\text{K}$. Find the cooling time constant. Energy balance: $mc\,dT/dt = -hA(T-T_ Given Information $h=20\ \text{W/m}^2\text{K}$ Physical…

Problem Statement State the Wiedemann-Franz law relating thermal and electrical conductivity of metals, and verify it for copper at $T=300\ \text{K}$. ($\kappa=400\ \text{W/m·K}$, $\sigma_{el}=6\times10^7\ \Omega^{-1}\text{m}^{-1}$) Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation…

Problem Statement Analyze the circuit: Analyze the circuit: Find the thermal resistance of the copper rod in Problem 2.136 and of a steel rod ($\kappa=50\ \text{W/m·K}$) of same dimensions. What is the total resistance in series? Thermal resistance (analogous to electrical resistance): $R_{th} = L/(\kappa A)$. $$R_{Cu} = \frac{0.5}{400\t Given Information See problem statement for…

Problem Statement Solve the Newton’s Laws / mechanics problem: State the principle of minimum entropy production (Prigogine) and explain when it applies. All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) This problem draws on fundamental physical principles. The key is to identify whi Given Information…

Problem Statement Solve the thermodynamics problem: Solve the thermodynamics problem: A copper rod (length $L=0.5\ \text{m}$, cross-section $A=4\ \text{cm}^2$, $\kappa=400\ \text{W/m·K}$) has ends at $T_1=100°\text{C}$ and $T_2=20°\text{C}$. Find the heat flux. Fourier’s law of heat conduction: $$\dot{Q} = -\kappa A\frac{dT}{dx} = \kappa A\frac{T_1-T Given Information See problem statement for all given quantities. Physical Concepts &…

Problem Statement Solve the quantum/modern physics problem: Solve the work-energy problem: Find the mean energy of photons in blackbody radiation at $T=300\ \text{K}$. The mean photon energy in blackbody radiation: $$\langle E\rangle = \frac{\int_0^\infty h\nu\,u(\nu)\,d\nu}{\int_0^\infty u(\nu)\,d\nu} = \frac{\sigma_{SB}T^4/c \cdot 4}{\text{(number density) Given Information See problem statement for all given quantities. Physical Concepts & Formulas This…

Problem Statement Solve the fluid mechanics problem: Solve the fluid mechanics problem: Find the radiation pressure of sunlight at Earth’s surface. Solar constant $I=1360\ \text{W/m}^2$. Radiation pressure (for absorbed radiation): $$P_{rad} = \frac{I}{c} = \frac{1360}{3\times10^8} = 4.53\times10^{-6}\ \text{Pa}$$ For perfectly reflecting surface, pre Given Information See problem statement for all given quantities. Physical Concepts &…

Problem Statement Solve the kinematics problem: Solve the kinematics problem: The sun’s surface temperature is $T=5800\ \text{K}$. Find the peak wavelength of solar radiation. Wien’s displacement law: $\lambda_{max} T = b$, where $b = 2.898\times10^{-3}\ \text{m·K}$. $$\lambda_{max} = \frac{b}{T} = \frac{2.898\times10^{-3}}{5800} = 5.0\times10^{- Given Information See problem statement for all given quantities. Physical Concepts &…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A body cools from $T_0=100°\text{C}$ to $T_\infty=20°\text{C}$ (ambient) following Newton’s law $dT/dt=-k(T-T_\infty)$ with $k=0.05\ \text{min}^{-1}$. How long to cool to $50°\text{C}$? Newton’s law of cooling (linearized Stefan-Boltzmann for small temper Given Information See problem statement for all given quantities.…